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Mathematical Analysis
Mathematical analysis is, simply put, the study of limits and how they can be manipulated. Starting with an exhaustive study of sets, mathematical analysis then continues on to the rigorous development of calculus, differential equations, model theory, and topology. Topics including real and complex analysis, differential equations and vector calculus can be discussed in this category.
2,575 Questions
How do you solve 5xy plus 7xsquared - 12y when x equals 2 y equals 1?
In the given expression you replace x by 2 and y by 1.
Thus 5xy + 7x2 - 12y = 5*x*y + 7*x2 - 12*y
= 5*2*1 + 7*22 - 12*1 = 10 + 28 - 12 = 26
if two signal input fed into circuit and gating one output
At any given time in hours after the family departs, the distance they have travelled will be 60t, while at the same time, the moving van will have covered a distance of 55(t + 1). The family will catch up when these two times are equal, or when 60t = 55(t + 1), or 60t - 55t = 55, or 5t = 55, or t = 55/5 hours = 11 hours.
How much greater is 4 to the power of 2 than 4 to the power of negative 2?
4 to the power of 2 is 42 = 16
4 to the power of negative 2 is 4-2 = 1/42 = 1/16
As far as "how much greater" - that depends on what you mean
If you mean what is the size of the difference...
16 - 1/16 = 15 15/16 = 15.9375 so 4² is 15.9375 greater than 1/4²
If you mean the ratio...
42/4-2 = 44 = 256 so 42 is 256 times the size of 4-2 or 255 times bigger
(i.e. 42 = 4-2 + 255·4-2)
What does the number 0408163245576318222527346277 mean?
It does not mean anything specifically. In a particular context it may have some meaning but you have chosen not to share that context with us.
What if you fell 4 classes in 9 grade?
If you fail 4 classes you will still be classified as a 9th grader.
What numbers add to give you 8 but multiply to give you 36?
4 + 2i*sqrt(5) and 4 - 2i*sqrt(5)
[where i is the square root of -1]
Given a+b=8, we have b=8-a.
Given ab = 36, we can substitute b=8-a to get a(8-a) = 36, or
a2 - 8a + 36 = 0
Using the quadratic formula gives the two possible answers, which accounts for the fact that a and b can be switched without affecting the problem.
How many kilometers are there in 820 meters?
There are 1000 metres in one kilometre. Therefore, 820 metres is equal to 820/1000 = 0.82 kilometres.
How do you compare one ratio against another ratio?
You divide them. For instance, to compare 1:3 against 3:5, treat them as fractions (1/3 and 3/5) and divide, in this case getting 5/9, which says that 1:3 is slightly more than half of 3:5. Remember that you can divide fractions by inverting one of them and multiplying - 1/3 divided by 3/5 is the same as 1/3 multiplied by 5/3.
Why is du infinitely small in calculus?
du refers to a differential part of u, which is infinitely small.
Why do we take a limit in math?
There are situations in mathematics where the value of a function is not defined for some value of the argument but you can get closer and closer to a fixed value. In such cases a limit may be the appropriate solution for finding an answer.
How do you apply laplace transform method to solve systems of ordinary DEs?
you apply the Laplace transform on both sides of both equations. You will then get a sytem of algebraic equations which you can solve them simultaneously by purely algebraic methods. Then take the inverse Laplace transform .
